A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses
318
Citation
0
Reference
10
Related Paper
Citation Trend
Abstract:
A weakest link theory for macroscopically homogeneous isotropic materials containing randomly oriented microcracks uniformly distributed in location is developed under the assumption that fracture depends only on the macroscopic stress normal to a crack plane. The function representing the number of cracks per unit volume failing at each value of normal stress is expanded as a Taylor series with coefficients determined from tensile test data. This function is used without additional assumptions to determine the probability of fracture under arbitrary (but not predominantly compressive) stress conditions. The results can be readily incorporated into a finite-element code to predict the failure probability of any structure to which the code applies.Keywords:
Brittleness
Plane stress
In this paper, we discuss five parameters that indicate the inhomogeneity of a stack of parallel isotropic layers. We show that, in certain situations, they provide further insight into the intrinsic inhomogeneity of a Backus medium, as compared to the Thomsen parameters. Additionally, we show that the Backus average of isotropic layers is isotropic if and only if $\gamma=0$. This is in contrast to parameters $\delta$ and $\epsilon$, whose zero values do not imply isotropy.
Zero (linguistics)
Cite
Citations (0)
Isotropy is a fundamental property of a diffuse sound field. Although several studies have proposed an isotropy indicator to quantify the extent of the isotropy of a sound field, what is not yet very clear is how to interpret the quantified isotropy using these indicators. This study aims to contribute to the understanding of the isotropy by (i) modifying an existing isotropy indicator based on the spherical harmonic expansion and (ii) presenting isotropic sound field model composed of a finite number of plane waves. Theoretical and numerical investigations show that a limited-degree isotropy can be established by using the isotropy indicator and the isotropic sound field model.
Cite
Citations (2)
Plane stress
Stress field
Principal stress
Stress–strain curve
Cite
Citations (10)
Cite
Citations (27)
Despite the tailorability of laminated fiber composites, the tendency has been to use lay-ups that more closely approximate an isotropic material. These so-called quasi-isotropic lay-ups are used so the structure or component fabricated from them can withstand loads oriented in many directions or perhaps accommodate an unexpected loading. Since there is so much literature associated with predicting the static and dynamic response of isotropic beams, plates, and shells, particularly in table look-up format, the question arises as to the applicability of these tabulated results to members made from quasi-isotropic composite materials. The purposes of this paper are: (1) to indicate the degree of isotropy exhibited by a certain quasi-isotropic sandwich construction, (2) to verify that standard isotropic strength-of-materials formulas can be used to predict the response of these quasi-isotropic components for certain loadings, and (3) to present numerical data for a particular material system. It is felt that even though the results are presented for a sandwich construction, they can be extended to quasi-isotropic lay-ups in general.
Cite
Citations (0)
In this paper, we discuss five parameters that indicate the inhomogeneity of a stack of parallel isotropic layers. We show that, in certain situations, they provide further insight into the intrinsic inhomogeneity of a Backus medium, as compared to the Thomsen parameters. Additionally, we show that the Backus average of isotropic layers is isotropic if and only if $\gamma=0$. This is in contrast to parameters $\delta$ and $\epsilon$, whose zero values do not imply isotropy.
Zero (linguistics)
Cite
Citations (0)
Uniform circular arrays are popular in direction finding applications because they show to be isotropic, i.e. they exhibit the same accuracy (in terms of the Cramer-Rao bound) at all possible planar look directions. We prove that this is not absolutely true if the constituent sensors are not isotropic. For instance, we specify how the anisotropic sensors should be directed and how many are needed in order to ensure an isotropic behavior of the array. We study, in more details, the performance of arrays of cardioid sensors, including anisotropic arrays of cardioid sensors.
Cite
Citations (7)
Stewart platform
Spatial configuration
Cite
Citations (40)
Plane stain assumption is widely used in the simulation of the distribution of stress and displacement around hydraulic fractures. According to the comparison of the solutions of elliptical fracture and plane stain fracture, the applicable conditions of plane strain assumption were discussed and the correction method was put forward. On the basis of the past research, a classical stress and displacement solution around a flat elliptical fracture was deduced, fulfilled and corrected. In comparison with the plain strain fracture solution, simulating results show that if taking plane strain assumption into consideration in the fracture height profile, the difference between the elliptical fracture solution and plane strain solution is negligible when the ratio between fracture length and fracture height is larger than 10, and the above critical value could be relaxed to 5 in some simulations which normal stress perpendicular to fracture face plays a decisive role. The plane strain fracture solution is accurate enough when the above critical value is satisfied, the correction of the plane strain fracture solution is needed when the length-height ratio is small. The correction charts of the additional initial stress of the horizontal well with an open-hole and the width of a single fracture were drawn under different length-height ratios. The fracture width of pseudo three dimension propagation models is easier to be modified by the correction charts.
Plane stress
Cite
Citations (14)
Plane stress
Strain (injury)
Constant (computer programming)
Cite
Citations (5)